Discrete quantum-behaved particle swarm optimization for the multi-unit combinatorial auction winner determination problem

Combinatorial auctions are efficient mechanisms for allocating resource in complex marketplace. Winner determination, which is NP-complete, is the core problem in combinatorial auctions. In this study we introduce a discrete quantum-behaved particle swarm optimization algorithm with a penalty function for solving the winner determination problem. Particle swarm optimization is a population-based swarm intelligence algorithm. A quantum-behaved particle swarm optimization is also proposed by combining the classical particle swarm optimization philosophy and quantum mechanics to improve performance of particle swarm optimization. Since, potential solutions are presented in binary space, we use a discrete version of quantum-behaved particle swarm optimization that introduced to discrete binary search space. And the penalty function has been applied to overcome constraints. We evaluated our approach in two steps. First we showed that the discrete quantum-behaved particle swarm optimization is applicable to the problem. Second we compared our approach with CASS (Combinatorial Auction Structured Search), Casanova, Genetic algorithm and OMAGA (Orthogonal Multi-Agent Genetic Algorithm) on eight standard test tests used by other researchers. The results showed that the discrete quantum-behaved particle swarm optimization in comparison to other algorithms is better on five test sets worse on one test set and same on two test sets. Therefore, we could conclude that our approach for solving the multi-unit combinatorial auction winner determination problem is suitable and could find the best solutions. © 2010 Asian Network for Scientific Information.